One of the biggest challenges of co-parenting after divorce is maintaining consistent rules and expectations across two households. You and your co-parent may have had different parenting styles when you were together. However, it's easier to maintain consistency when everyone's in the same home.
The parent who has custody of the kids the majority of the time is likely to have more and stricter rules for them than their co-parent who may only see them on weekends and holidays. The parent who spends less time with the kids may be more likely to let them stay up late (particularly on nonschool nights), order in food rather than cook and leave the tidying up to the housekeeper. One parent may also be more permissive because they're vying to be the favorite.
It's typically best for kids when their parents have the same expectations about behavior, chores, homework and bedtimes across both households. However, ex-spouses rarely parent precisely the same way. That's okay.
It's wise to agree on the big things, like making school a priority and whether your kids are old enough to date. However, kids can learn to deal with different rules and practices in their two homes. It's more important that each parent be consistent with their own rules.
Once you and your co-parent accept that you have different rules and expectations, you can be upfront with each other about what they are, and the kids are less likely to take advantage of you. If you know that your co-parent lets them watch an hour of TV a night, even if you allow no TV on school nights, your kids won't try to convince you that they get to watch unlimited TV at their mom's or dad's house.
Co-parents can and should be able to have rules and expectations when it comes to how their kids are raised. These can be outlined in your co-parenting plan. Working out a plan that the two of you can both abide by can help minimize conflicts and provide your kids with the reassurance that their parents have shared goals and expectations for them even though they're no longer together.